The largest seismic event ever recorded on Mars, with a moment magnitude of 4.7±0.2, is the first event to produce both Love and Rayleigh wave signals. We measured their group velocity dispersion between about 15 s and 40 s period and found that no isotropic depth-dependent velocity model could explain the two types of waves wave simultaneously, likely indicating the presence of seismic anisotropy. Inversions of Love and Rayleigh waves yielded velocity models with horizontally polarized shear waves traveling faster than vertically polarized shear waves in the top 10 km – 25 km. We discuss the possible origins of this signal, including the preferred orientation of anisotropic crystals due to shear deformation, alignment of cracks, layered intrusions due to an impact, horizontal layering due to the presence of a large-scale sediment layer on top of the crust, and alternation of sedimentation and basalt layers deposits due to large volcanic eruptions.